Average Error: 37.0 → 37.0
Time: 3.3s
Precision: binary64
\[\sin \left(x + \varepsilon\right) - \sin x\]
↓
\[\sin \left(x + \varepsilon\right) - \sin x\]
\sin \left(x + \varepsilon\right) - \sin x
↓
\sin \left(x + \varepsilon\right) - \sin x
double code(double x, double eps) {
	return ((double) (((double) sin(((double) (x + eps)))) - ((double) sin(x))));
}
↓
double code(double x, double eps) {
	return ((double) (((double) sin(((double) (x + eps)))) - ((double) sin(x))));
}

Error

Bits error versus x

Bits error versus eps

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 37.0

    \[\sin \left(x + \varepsilon\right) - \sin x\]

  2. Final simplification37.0

    \[\leadsto \sin \left(x + \varepsilon\right) - \sin x\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x eps)
  :name "(- (sin (+ x eps)) (sin x))"
  :precision binary64
  (- (sin (+ x eps)) (sin x)))